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Maximum Alternating Subsequence Sum
The alternating sum of a 0-indexed array is defined as the sum of the elements at even indices minus the sum of the elements at odd indices.
- For example, the alternating sum of
[4,2,5,3]
is(4 + 5) - (2 + 3) = 4
.
Given an array nums
, return the maximum alternating sum of any subsequence of nums
(after reindexing the elements of the subsequence).
A subsequence of an array is a new array generated from the original array by deleting some elements (possibly none) without changing the remaining elements’ relative order. For example, [2,7,4]
is a subsequence of [4,2,3,7,2,1,4]
(the underlined elements), while [2,4,2]
is not.
Example 1:
Input: nums = [4,2,5,3] Output: 7 Explanation: It is optimal to choose the subsequence [4,2,5] with alternating sum (4 + 5) - 2 = 7.
Example 2:
Input: nums = [5,6,7,8] Output: 8 Explanation: It is optimal to choose the subsequence [8] with alternating sum 8.
Example 3:
Input: nums = [6,2,1,2,4,5] Output: 10 Explanation: It is optimal to choose the subsequence [6,1,5] with alternating sum (6 + 5) - 1 = 10.
Constraints:
1 <= nums.length <= 105
1 <= nums[i] <= 105

Program:
class Solution:
def maxAlternatingSum(self, nums: List[int]) -> int:
ans = 0
direction = 'down'
n = len(nums)
for i in range(n-1):
if direction == 'down' and nums[i] >= nums[i+1]:
ans += nums[i]
direction = 'up'
elif direction == 'up' and nums[i] <= nums[i+1]:
ans -= nums[i]
direction = 'down'
if direction == 'up':
return ans
return ans + nums[-1]
Credit : Here
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